Premier League: Fulham 1 Chelsea 3
The forward notched his second hat-trick of the season, having achieved the feat for Germany against Sweden in October, and doubled his Chelsea tally to six league goals in 2013-14 following his second-half treble at Craven Cottage on Saturday.
Hosts Fulham had the better chances in the opening period, but failed to take them and were made to pay as the visitors moved up through the gears after the break.
Schurrle, ably assisted by Eden Hazard and Fernando Torres, finished all three efforts clinically as Chelsea extended their unbeaten run to 13 league games, despite John Heitinga's late consolation.
Victory, combined with Arsenal's defeat against Stoke, sees Chelsea open up a gap at the top of the table, while Fulham remain rooted to the bottom after an eighth league game without a win.
Following their midweek UEFA Champions League trip to Turkey, Premier League leaders Chelsea took their time to settle into the game and were lucky not to be behind in the third minute as Clint Dempsey wasted a great chance.
Pajtim Kasami forced his way past Branislav Ivanovic on the left and drilled a cross into the penalty area for the unmarked American, playing the last game of his loan spell, but the 30-year-old could not direct his header on target from six yards.
Chances were at a premium for both sides in a half bereft of quality, with only Kasami forcing a save from either goalkeeper with a low free-kick in the final five minutes that Petr Cech held easily.
Chelsea quickly put their poor first-half display behind them as Schurrle opened the scoring seven minutes after the break.
Hazard played a weighted pass over the top of the Fulham defence for the German to run onto, he cut across Dan Burn and slotted past Maarten Stekelenburg from the edge of the penalty area.
Torres should have doubled Chelsea's lead just before the hour after more excellent work from Hazard, but the 29-year-old saw his header at the back post deflect off Kieran Richardson.
With 65 minutes played, Schurrle added his second goal, with Hazard again involved. The Belgian escaped the attentions of Heitinga before rolling a perfect pass into Schurrle and he fired low beyond Stekelenburg.
Schurrle's hat-trick was complete three minutes later as the forward made no mistake with a calm finish after being played in by Torres.
Fulham netted a consolation with 16 minutes to play as Darren Bent knocked down a Lewis Holtby corner and Heitinga poked the ball beyond Cech from close range.